Robust utility maximization for complete and incomplete market models

We investigate the problem of maximizing the robust utility functional <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$\inf_{Q \in \mathcal{Q}} E_Qu(X)$</EquationSource> </InlineEquation>. We give the dual characterization for its solution for both a complete and an incomplete market model. To this end, we introduce the new notion of reverse f-projections and use techniques developed for f-divergences. This is a suitable tool to reduce the robust problem to the classical problem of utility maximization under a certain measure: the reverse f-projection. Furthermore, we give the dual characterization for a closely related problem, the minimization of expenditures given a minimum level of expected utility in a robust setting and for an incomplete market. Copyright Springer-Verlag Berlin/Heidelberg 2005